Fall
2013 
Mtg
# 
Agenda For Class Meeting
(What is Planned / What Happened) 
Homework Assignment/Tasks
(To be completed before the next class
meeting) 

AUG
19 



[1] 
Activity
Getting a Little Discrete
examples of
Discrete Math topics, background information

Assignment
Getting There ASAP

[2] 
Activity
Game of Sprouts
how to play, rules
Notes Graph Theory Basics:
Vocabulary &
Counting
vertex, edge, degree, strategies for counting 
Question
How Many Moves?
Is it possible to predict the maximum number of moves that can be
played in a Sprouts game based on how many vertices at the start of the
game?


AUG
26 
[3] 
Activity
Analyzing The Game of Sprouts
quantifiable differences, collecting data, looking for patterns,
describing patterns

Research
Leonard Euler
write 3 sentences about Euler's life and why he is considered one of
the greatest mathematicians

[4] 
Activity
The Euler Characteristic
quantifiable
differences, looking for patterns
Notes
Describing Structures in Graphs
adjacent, planar, complete

Crossword
Talking Graph Theory
facts about Euler, graph theory vocabulary

[5] 
Notes The
"Essence" of a Graph
equivalent representations,
isomorphisms,
planar
Activity
Water Puzzle
draw a graph that represents the game

Research
The FourColor Problem
6 sentences (who, what, where, when, why,
how)

[6] 
Audio Clip
Solving or Proving? The 4Color Problem
Activity
Coloring Maps
Four Color
Problem, algorithms

Activity
Coloring Maps
Four Color
Problem, algorithms


SEP
02 

LABOR DAY HOLIDAY 
[7] 
Activity
Tracing a Graph
Seven Bridges of Königsberg & Eulerian paths,
necessary & sufficient conditions

Research
The Traveling Salesman Problem
6 sentences (who, what, where, when, why,
how)

[8] 
Notes/Video
Movement in Graphs:
Paths & Circuits
path, circuit, necessary &
sufficient conditions


[9] 
Notes
Traveling Salesman Problem & Algorithms
Nearest Neighbor, Cheapest Link,
strategies, establishing simple repeatable
steps/clear process

Activity
TSP in Florida
find
Hamiltonian circuits using the Nearest Neighbor algorithm first then the
Cheapest Link algorithm


SEP
09 
[10] 
Review
TSP Applications & Algorithms
routing, construction

Read
Splitting Terrorist Cells

[11] 
Discuss
Connectivity in Graphs
how to measure, bridges, cut vertices, pieces,
applications

Crossword
Graph Theory Vocabulary Review

[12] 
Review
Graph Theory Fundamentals
Cheapest Link & Nearest Neighbor algorithms, planar, paths,
circuits, complete, adjacent, isomorphic

Sample Test Questions
Graph Theory Fundamentals
[Solutions]

[13] 
Test
Graph Theory Fundamentals
Collect Homework & Classwork

Assignment
Sudokus  A Glimmer of Algorithms


SEP
16 
[14] 
Discussion
Navigating Sudoku Using Algorithms
practice the
sudoku algorithm discussed in class
Video/Activity
Getting There Efficiently
Dijkstra's Algorithm

Assignment
Finding the Shortest Path in Graphs [Numb3rs]
complete
questions #14

[15] 
Notes
Examining Dijkstra's Byproduct
subgraphs,
trees, minimal spanning trees
Activity
Modeling: Getting Things Done
flow, directed
edges & digraphs, modeling

Assignment
Turner Construction
find the least
amount of time it will take to complete the construction project

[16] 
Notes
Navigating Flow in Graphs
critical
paths, source, sink, quantifying capacity, flow paths & max flow

Assignment
Finding the Flow
map the max
flow for a digraph

[17] 
Notes
Navigating Flow in Graphs [Numb3rs]
quantifiable differences, starting backwards, exclusionary approach

Assignment
How Much Can You Flow?
develop an
algorithm to determine the maximum flow in a digraph


SEP
23 

FACULTY INSERVICE DAY 
[18] 
Video
Applications of Graphs & Algorithms
work flow &
queues

Assignment
Connecting the Campus

[19] 
Activity
Increasing Electricity Flow

Sample Test Questions
More Graph Theory & Algorithms
[Solutions]

[20] 
Test
More Graph Theory & Algorithms
Collect Homework & Classwork

Assignment
Is It Prime?
If all you had was a basic calculator, paper,
and pencil, explain how you would figure out that 6,887 is not a prime
number.


SEP
30 
[21] 
Notes
Getting Into Algorithms
multiplication & division, efficiency, prerequisites, Rubik
Cubes, divisibility

Research
The Sieve of Eratosthenes

[22] 
Notes
Setting the Stage for Number Theory
partitioning & factoring, uniqueness of prime factorization, sifting
for primes

Research
Goldbach's Conjecture
Who? What?
Where? When? Why? How?

[23] 
Video Getting
Primed for Number Theory
distribution of primes,
π(n) function, establishing bounds,
natural log, comparing quantities

Research
Mersenne Primes
Who? What?
Where? When? Why? How?

[24] 
Video
Getting to Know Numbers
divisibility, visualizing patterns, proof, Collatz's Question

Research
Perfect Numbers & Pentagonal Numbers


OCT
07 
[25] 
Notes Figurative
Numbers: Patterns Galore
triangular, square, pentagonal, Gauss & partitions

Research
Fibonacci
6 sentences (who, what, where, when, why,
how)

[26] 
Notes Sequences:
Gauss & Fibonacci
recursive definitions, partial sums
Activity
Generating Sequences in Excel
laptop cart etiquette, basic features

Crossword
Number Theory Review

[27] 
Notes Number
Symbols & Zero
recycle vs. create new, place value, alternate base/groupings
Activity
Generating Sequences in Excel

Sample Test Questions
Number
Theory Basics & Algorithms [Solutions]

[28] 
Test Number
Theory Basics & Algorithms
Collect Homework & Classwork

Assignment
Avoiding Friday the 13th


OCT
14 
[29] 
Activity
Using Modular Arithmetic:
Friday the 13th
modeling
repeating cycles, finding congruences

Assignment
Predicting the Future


FROSH SERVICE DAY / PSAT / SENIOR WORKSHOPS 

OCTOBER BREAK  Classes Do Not Meet 


OCT
21 
[30] 
Notes
Into the Mod: Check Digit Applications
algorithms, congruence, ISBN10 & ISBN13 numbers

Research
UPC Number Check Digits

[31] 
Notes/Activity
Sneaky Scrambling Algorithms
counting methods, scrambling via modular arithmetic & geometry

Read
Cryptography: Secret Writing pp 1128

[32] 
Notes Only Two
Options: Transposition & Substitution
scrambling vs. replacing, algorithms, reversibility

Read
Cryptography: Secret Writing pp
2956

[33] 
Notes/Activity
Going Backwards: Unscrambling
modular arithmetic & inverse operations

Assignment
Solving Equations in Modular Arithmetic



NOV
04 
[37] 
Notes
Mathematics of Substitution: Forwards
methods for scrambling the alphabet, onetoone correspondence

Read
Cryptological Mathematics pp 2734

[38] 
Activity
Automating Substitution Ciphers
text & chart referencing functions, number to text conversions,
uppercase vs. lowercase

Assignment
Monoalphabetic Ciphers

[39] 
Activity
Automating Substitution Ciphers: Generating Alphabets
number to text conversions, replicating patterns using mod


[40] 
Activity
Automating Substitution Ciphers: Affine Shuffles
text & chart referencing functions

Video
CodeBreakers: Bletchley Park's Lost Heroes


NOV
11 
[41] 
Quiz
CodeBreakers: Bletchley Park's Lost Heroes
Activity
Affine Ciphers
additive vs. multiplicative, keys, modular inverses

Read Cryptological Mathematics
pp 7681

[42] 
Activity
Polyalphabetical Ciphers
keys, modular patterns, Enigma Machine

Assignment
Polyalphabetic Ciphers

[43] 
Notes
How Secure Is Your Cipher System?
brute force &
key options, strategies for breaking

Read
Cryptological Mathematics
pp 103108

[44] 
Notes
Increasing Complexity & Subtle Twists
Hill
Ciphers/matrix algebra, steganography

Research
RSA Encryption
6 sentences (who, what, where, when, why,
how)


NOV
18 
[45] 
Notes 
Understanding Public Key Encryption: RSA
modular arithmetic, primes, finding inverses, public and private
keys 
Sample Test Questions
Cipher Systems
& Spreadsheets [Selected
Solutions]

[46] 
Test
Cipher Systems & Spreadsheets
Collect Classwork & Homework

Assignment
Design Your Own Cipher System (example)

must have
substitution and transposition

not more
than 6 steps in complexity

originality/creativity (5pts max)

communication/presentation (5pts max)

[47] 
Cipher System Project 
Introduction & Information
scope, expectations, guidelines, specifications 
Cipher System Project 
[48] 
Cipher System Project 
Organizational Workday
organize homepage, synthesize ideas for substitution &
transposition, establish timeline/key dates, assign responsibilities 
Cipher System Project 



DEC
09 
[54] 
Cipher System Project 
Presentations 
Activity TwoPlayer Games:
Dr. Markov Find a
Winning Strategy for Saving the Dog 
[55] 
Review Graph Theory 

[56] 
Review Number Theory 

[57] 
Review Cryptography 


DEC
16 
[58] 
Course/Teacher Evaluation
Semester Reflection/Final Exam Essay Question 
Sample
Final Exam 

SEMESTER EXAMS  SOCIAL SCIENCE & MATHEMATICS 

SEMESTER EXAMS  ENGLISH & RELIGIOUS STUDIES 

SEMESTER EXAMS  LANGUAGE & SCIENCE 
